Flexpad is a highly flexible display interface. It introduces a novel way of interacting with flexible displays by using detailed deformations. Using a Kinect camera and a projector, Flexpad transforms virtually any sheet of paper or foam into a flexible, highly deformable and spatially aware handheld display. It uses a novel approach for tracking deformed surfaces from depth images in real time. This approach captures deformations in high detail, is very robust to occlusions created by the user’s hands and fingers and does not require any kind of markers or visible texture. As a result, the display is considerably more deformable than previous work on flexible handheld displays, enabling novel applications that leverage the high expressiveness of detailed deformation. We illustrate these unique capabilities through three application examples: curved cross-cuts in volumetric images, deforming virtual paper characters, and slicing through time in videos. Results from two user studies show that our system is capable of detecting complex deformations and that users are able to perform them fast and precisely.